Even in the "cleanest" case prepared correctly, all sorts of things can go wrong on the USCIS end - but here we don't actually know whether this is a "clean" (problem-free) case or not. At the very least, the couple needs to sit down for a consultation with a qualified immigration lawyer to determine what, if any, problems might exist.
The fact that the wife overstayed her visa doesn't necessarily mean the case will be a problem. As long as she entered legally with a visa (was "inspected" by an immigration officer), she may be able to get a green card here in the U.S. even if this visa has since expired. However, all sorts of things might cause problems: not only criminal background, but health, finances of the couple in the U.S., memberships in certain organizations abroad, restrictions accompanying prior U.S. visa status (for instance, people who entered legally on a J-1 often have a problem). There are several other things which may cause issues, and should be explored with a qualified attorney. If there are any problems at all, there is no question that the case should be handled by an attorney.
If after doing this, the case appears to be "clean," the next question is how much risk the couple wants to assume. The process is complex, and since the wife is without status they may only have one chance at doing this correctly - if the case is denied either through a mistake in completing the forms or through a USCIS error that the couple doesn't know how to address, more and more often the case is referred for legal proceedings to remove the spouse who is without status from the U.S. these days.
Often a denied marriage petition can be renewed either before proceedings or even during - of course, this depends on the reason for denial. I've had couples approach me to handle re-files on denied case where they caused themselves so much trouble on the first case (usually by misrepresenting or failing to disclose something that wouldn't have been an insurmountable problem anyway) that there wasn't much I could do to fix it - or it cost them many thousands more to fix things at that point.
Once past the immigration risk, look at the financial risk - even if done without an attorney, this type of case will cost about $1700-$1800 in fees ($1465 filing, a $200-$400 medical exam, passport photos, postage). Legal fees depend on the case/lawyer/location/services offered, etc., but are normally slightly less than almost that much again. Assuming a second case needs to be filed because the first case isn't approved, and that you are ABLE to file a second case, the cost will be more than doing right the first time with a lawyer not to mention the delay.
The couple should schedule a consultation with a lawyer to get all of the facts about their case, and then make an informed decision.
I agree with the other poster. At the very least sit down with an attorney and lay all of the facts on the table. This way you can determine if it is a clean case or not, and if you want to retain an attorney or not. When we have such consultations many of us include the fee into our flat fees, so if we end up handling the case, the consultation is essentially credited back and you only pay the regular flat fee for doing this.
I don't believe that all cases require an attorney, but I do think there is much value in at least understanding the process better, knowing that your filing is complete, and getting some peace of mind that you should be ok.
Generally, a foreign national who entered the United States with a valid visa may adjust his or her status through marriage to a U.S. citizen, even if the non-immigrant status has expired. Having said that, hiring an attorney will be very helpful in case mistakes are made by USCIS or the adjudicating officers. You should keep in mind that although you are eligible to adjust your status within the United States, administrative and human erros may significantly delay or cause your case to be denied. If you were represented by an immigration attorney, you enjoy the added security that a professional is supervising your case.
For example, many clients who are in your position may not know that if you leave the U.S. after overstaying the non-immigrant visa for more than 180 days, you may be barred from being able to return to the U.S., EVEN IF your green card petition/application is currently pending. Many clients obtained the travel document (advance parol) and traveled out of the U.S. thinking that the travel document gives them permission to do so. If represented, the attorney will properly advise the client not to travel. This is but one important benefits of having an attorney handle your immigration case for you.